<header>
    判断是否有解？
</header>
<p>
    设线性方程组为
    <span class="oneline">
        <code>
            ["equationSet",
                ["join",["rightBottom","a","11"],["rightBottom","x","1"]," + ",["rightBottom","a","12"],["rightBottom","x","2"]," + ... + ",["rightBottom","a","1n"],["rightBottom","x","n"]," = ",["rightBottom","b","1"]],
                ["join",["rightBottom","a","21"],["rightBottom","x","1"]," + ",["rightBottom","a","22"],["rightBottom","x","2"]," + ... + ",["rightBottom","a","2n"],["rightBottom","x","n"]," = ",["rightBottom","b","2"]],
                "                                               ... ... ... ...",
                ["join",["rightBottom","a","s1"],["rightBottom","x","1"]," + ",["rightBottom","a","s2"],["rightBottom","x","2"]," + ... + ",["rightBottom","a","sn"],["rightBottom","x","n"]," = ",["rightBottom","b","s"]]
            ]
        </code>
    </span>
    引入向量
    <span class="oneline">
        <code>
            ["join",
                ["rightBottom","α","1"],
                " = ",
                ["matrix",[
                    [["rightBottom","a","11"]],
                    [["rightBottom","a","21"]],
                    ["⁝"],
                    [["rightBottom","a","s1"]]
                ]],
                " , ",
                ["rightBottom","α","2"],
                " = ",
                ["matrix",[
                    [["rightBottom","a","12"]],
                    [["rightBottom","a","22"]],
                    ["⁝"],
                    [["rightBottom","a","s2"]]
                ]],
                " , ... ,",
                ["rightBottom","α","n"],
                " = ",
                ["matrix",[
                    [["rightBottom","a","1n"]],
                    [["rightBottom","a","2n"]],
                    ["⁝"],
                    [["rightBottom","a","sn"]]
                ]],
                " , ",
                " β = ",
                ["matrix",[
                    [["rightBottom","b","1"]],
                    [["rightBottom","b","2"]],
                    ["⁝"],
                    [["rightBottom","b","s"]]
                ]]
            ]
        </code>
    </span>
    于是线性方程组可以改写成向量组
    <span class="oneline">
        x<sub>1</sub>α<sub>1</sub> +
        x<sub>2</sub>α<sub>2</sub> + ... +
        x<sub>n</sub>α<sub>n</sub> = β
    </span>
    显然，线性方程组有解的充分必要条件为向量β可以表出向量组
    α<sub>1</sub>,α<sub>2</sub>, ... ,α<sub>n</sub>
    的一个线性组合。
</p>
<p>
    用秩的概念，可以表述为：
</p>
<p>
    <span class="title">
        定理（线性方程组有解判别定理）
    </span>
    线性方程组有解的充分必要条件为它的系数矩阵
    <span class="oneline">
        A =
        <code>
            ["matrix",[
                [["rightBottom","a","11"],["rightBottom","a","12"],"...",["rightBottom","a","1n"]],
                [["rightBottom","a","21"],["rightBottom","a","22"],"...",["rightBottom","a","2n"]],
                ["⁝","⁝"," ","⁝"],
                [["rightBottom","a","s1"],["rightBottom","a","s2"],"...",["rightBottom","a","sn"]]
            ]]
        </code>
    </span>
    与增广矩阵
    <span class="oneline">
        <code>["upLine","A"]</code> =
        <code>
            ["matrix",[
                [["rightBottom","a","11"],["rightBottom","a","12"],"...",["rightBottom","a","1n"],["rightBottom","b","1"]],
                [["rightBottom","a","21"],["rightBottom","a","22"],"...",["rightBottom","a","2n"],["rightBottom","b","2"]],
                ["⁝","⁝"," ","⁝"],
                [["rightBottom","a","s1"],["rightBottom","a","s2"],"...",["rightBottom","a","sn"],["rightBottom","b","s"]]
            ]]
        </code>
    </span>
    有相同的秩。
</p>